Problem 1 Multiples of 3 and 5

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.



In [10]:

    
def frizz_buzz(number):
    """
    Calculates the sum of the all the multiples of 3 or 5 of `n`.
    @param n -- a non-negative integer
    @return integer
    """
    mutliples_of_three_and_five = lambda x: x if (x % 5 == 0) or (x % 3 == 0) else 0 
    return sum(map(mutliples_of_three_and_five, range(number)))



In [11]:

    
%timeit frizz_buzz(1000)









    



1000 loops, best of 3: 334 µs per loop



In [12]:

    
import time
 
start = time.time()

result = frizz_buzz(1000)

elapsed = time.time() - start
 
print "result %s returned in %s seconds" % (result,elapsed)









    



result 233168 returned in 0.000526905059814 seconds

Problem 2 Even Fibonacci numbers

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.



In [25]:

    
def fib(n):
    """
    Calculates the `nth` value of the fibbonacci sequence.
    @param n -- a non-negative integer
    @return integer
    """
    # base case
    if n < 2:
        return n
    return fib(n-1) + fib(n-2)



In [26]:

    
from unittest import TestCase

class test_if_fib_outptus_fibonacci_sequence(TestCase):
    
    def setUp(self):
        self.input = range(10)
        self.output = [0, 1, 1, 2, 3, 5, 8, 13 , 21, 34, 55]
    
    def test_if_fib_correctly_ouptuts_values_less_than_10(self):
        self.AssertEqual(self.output, [fib(i) for i in self.input])

if __name__ == '__main__':
    unittest.main()



In [ ]:

    
assert fib(4) == 3
assert fib(8) == 21



In [91]:

    
def even_fib(limit):
    """
    Calculates the sum of even values in the fibbonacci sequence up to the given limit.
    @param limit -- a non-negative integer
    @return integer
    """
    limit += 2
    total = 0
    for n in xrange(2, limit):
        value = fib(n)
        if value % 2 == 0:
            total += value
    return total



In [86]:

    
from unittest import TestCase

class TestEvenFib(TestCase):
    
    def setUp(self):
        self.input = 4000000
        self.even_fib_sum_of_10 = 44
        self.even_fib_sum_of_4_millio
    
    def test_even_fib_outputs_correct_sum(self):
        self.assertEqual(self.input, even_fib(self.output))
        
if __name__ = 'main':
    unittest.main()









    



  File "<ipython-input-86-af4cd5901713>", line 7
    self.output =
                  ^
SyntaxError: invalid syntax



In [92]:

    
even_fib(10)









    Out[92]:





44



In [94]:

    
sum([x for x in [1, 2, 3, 5, 8, 13, 21, 34, 55, 89] if x%2 ==0])









    Out[94]:





44



In [ ]: